82 interest and identity convergence for equitable ... · mathematical teaching practices as...

The Mathematics Educator

2017 Vol. 26, No. 1, 56–82

Interest and Identity Convergence for

Equitable Mathematics’ Teaching:

Reflections on the Interplay of the

Institutional and Individual on Teacher

Development and Action

Tara Meister

Propelled by Maxine Greene’s (1988) continuum of freedom from

normative structures to critical consciousness and action, I illuminate

the institutional and individual influences on teacher development

and action in mathematics teaching. I focus on the question: What

barriers and openings, both individually and institutionally, spur

teachers to consider equitable mathematical teaching practices as

important to pursue with commitment? Reflecting on the broad

cultural features that uphold mathematical inequities, factors that

inform mathematical contexts, and constructions of individual

identity, I contemplate avenues to enter meaningful, asset-oriented

growth for white teachers in particular toward equity practices in

mathematics. I argue that linear frameworks, such as white privilege

and racial identity development, do not provide the required

reflection and action steps for transformation. Rather, the nuance of

societal conditions and dynamics of individual identity must be

examined in depth by teachers and mathematics classrooms to

progress toward equity. Teachers’ identity convergence, the moral

imperative to understand the self and others, will prompt institutional

change before interest convergence (Bell, 2005a) necessitates it, as

the economic benefits of mathematical equity are not immediately

apparent.

Year after year, measures depict the growing achievement

gap between African-American and Latinx students and white

students, demonstrating more than half a standard deviation of

difference in mathematics by Kindergarten (Espinosa, 2005).

The discourse around mathematical achievement and inequities

centers on gap-gazing (Gutiérrez, 2012), or blame-shifting, to

Tara Meister is a PhD student in Curriculum and Instruction at the

University of Denver. Her work interrogates the historically-rooted

influences of race and power in education, including the interrelationships

between structural and individual factors.

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57

move responsibility from policy makers, teachers, and

administrators. Rather than acknowledging the myriad

influences on achievement in the construction of tests and the

learning environment itself (Au, 2013), achievement discourse

uses deficit thinking that focuses on missing skills or traits to

discuss students of color and their families (Aguirre, Mayfield-

Ingram, & Martin, 2013; Martin, 2007; Davis & Martin, 2008).

Positioning Black students as mathematically illiterate and

lower achieving reifies them “as particular kinds of students

and learners” (Martin, 2007, p. 17), namely, “inferior and

lacking in intelligence” (p. 16) without considering other

explanations for their mathematical disengagement, challenges,

or resistance. Moses and Cobb (2001) considered mathematical

literacy the civil rights’ issue of the current age because of its

contributions to technological advances, necessity for college

admittance, and opening of economic options. Because of

demographic shifts, teachers must understand social and racial

realities required for equitable mathematical instruction (Wang,

Castro, & Cunningham, 2014).

Ignoring the causes of achievement inequities poses major

obstacles to equitable teaching and learning. While

reductionistic mentalities behind inequity apply to Latinx

communities and some Asian communities (Paik, Kula, Saito,

Rahman, & Witenstein, 2014), I focus predominately on Black

students. Achievement data distorts Black and Latinx students

in particular, considering them insufficient compared to a white

norm (Davis & Martin, 2008; Martin, 2012) rather than with

strength-based conceptions of their cultural capital, such as

their ability to navigate multiple communities, speak various

languages or styles, and resist oppression (Yosso, 2005).

Distortion develops a “massified” consciousness (Freire, 2011)

wherein individuals do not realize the complexity positioning

certain racial groups as less capable (Frankenstein, 1983, p.

19). Thus, Martin (2007) claimed if teachers do not understand

the social realities of students, the way students can use

mathematics as power, and the role of racial identities in

mathematics learning to move past deficit-based perspectives

of students, they are not qualified to teach Black students.

Disruption of race-based hierarchies of capability must go

Interest and Identity Convergence for Equitable Mathematics’ Teaching

58

beyond teachers’ good intents. It entails deep examination of

their identities in relation to their students and the practices,

systems, and thinking behind inequity.

Despite critical interrogation, I use an asset-oriented view

of teachers by situating their realities within structures to

position them as agents capable of the reflection and practices

required for equitable teaching. Teachers exist within

institutional structures such as schools, university programs,

teacher communities, and school districts that permeate

individual consciousness and impact how they see and

construct normative practices. Because of the interplay

between individual and institution, teachers must probe the

features of the institutions. Therefore, I first focus on the

question: What barriers and openings, both individually and

institutionally, influence teachers to consider equitable

mathematical teaching practices as important to pursue? To

consider teacher development and action, I use Greene’s (1988)

continuum from Dialectic of Freedom for naming structures,

resisting them, and engaging in praxis—reflection and action—

to transform systems and selves (Freire, 2011). Second, I

answer: What avenues exist to enter meaningful, asset-oriented

growth beyond limited frameworks for white teachers toward

equity practices in mathematics?

Equity Definitions/Grounding

To enter the challenging spaces of equity work and the

required critical self-reflection, I start by grounding my conceptions of the individual and institutional components of

equity and racism. For Aguirre et al. (2013), equity involves

considering each student in the context of their humanity to

provide access, opportunity, and positive identity development.

Positive identity development entails building experiences and

reflections that build from student backgrounds and strengths.

Equity requires teachers to provide differential educational

practices, so each student “learn[s] rich mathematics that

fosters meaning making, empowers decision making, and

critiques, challenges, and transforms inequities and injustices”

(Aguirre et al., 2013, p. 9). Equity work includes both

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institutions and individual mentalities toward individuals or

groups to either view cultures and backgrounds as an asset or

deficit. Institutionally, normative structures of educational

accountability based chiefly on standardized tests serve to reify

inequity. Likewise, my conceptions of racism involve both the

individual and the institutional. Jones’ (2000) definition of

racism includes personally mediated beliefs and prejudices and

how institutions like educational systems serve groups

differentially. White supremacy encompasses the perceptions

and institutions that position white people as superior, abler, or

more deserving of success and opportunity.

Greene’s critical consciousness, reflective resistance,

and action. For the bulk of this piece, I name institutional and

individual features constructing racial inequity in mathematics

teaching and learning. Greene (1988) considered seeing and

naming the world as a necessary practice to push past the veil

of the familiar, to understand what goes on underneath

normative veneers, and to connect the individual experience

within macro structures and ideologies. I deconstruct cultural,

institutional, and individual features that mutually reinforce

racial inequity. By engaging with the various levels of

inequity’s operation, I interrogate the world to understand its

operation, build critical consciousness, and lead to reflective

resistance—the connecting of self to the world. While

acknowledging the nuance of inequity, I concentrate on laying

the groundwork for reflective resistance in response. Thus, this

piece may be read through the aim of reflective resistance with

questions such as the following in the reader’s mind: How do

the ideas emerge in my experiences and worldview? What

concepts or ideas bump against what I have previously known

and/or cause me discomfort? Why? What question(s) come up

for me?

As a product of U.S. schools and society, I breathed the

normative discourses of colorblindness, meritocracy, and

Manifest Destiny, accepting them and applying them to my

experiences in my insulated childhood community. Especially

in middle school and beyond, various ruptures occurred for me:

talking to high school classmates from the Middle East about

9/11, living with all Native American students two summers


60

and with students of color from New York City another, and

attending a private liberal arts college with a perceptible bloc

of whiteness. My critical consciousness and the actions that

emanate from my reflexion and experiences cycle and shift, as

I embrace challenges to my comfort and beliefs as necessary to

be in process against white supremacy. From self-inquiry

grounded in critical consciousness, we can undertake deliberate

actions to alter our own perceptions and to transform our

classrooms, curriculum, instruction, and, together, institutions

toward equity.

Cultural Features Upholding Mathematical Inequity

This section charts the various cultural factors that

influence the existence and maintenance of mathematical

inequities. Mathematics instruction is historically rooted in

legacies of slavery and colonialism and its features are

institutionally embedded through pedagogy, curriculum, and

accountability mechanisms. These contextual features, then,

construct individual mentalities and actions that often serve to

reinforce inequity.

Historical Consciousness within Individuals and

Institutions

First, I consider the overarching cultural terrain within

which institutions and individuals operate. Mathematics is not

neutral content and pedagogical terrain (Leonard, Brooks,

Barnes-Johnson, & Berry, 2010); instead, it is entrenched in the

“historical consciousness” of slavery, colonialism, and

imperialism (West, 1989, p. 69). Attitudes and practices

emerge out of historical context to become “so fixed as to

become institutional” (Dewey, 1938, p. 29), maintaining the

status quo. The status quo includes institutionalized features,

such as assessment socialization, achievement orientation,

banking education, and colorblind racism and individual

mentalities that become normative, including deficit mindsets,

racism, and beliefs in meritocracy.

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The “authoritative discourse” (Lensmire et al., 2013, p.

428), or common discourse of everyday language, becomes

institutionalized, creating a patterned environment of comfort

where individuals operate. While easiest to operate within

normative patterns, teachers retain the creativity, agency, and

power to interrogate norms toward equity. However, without

critical inquiry, institutions become hegemonic, “so quiet, so

seductive, so disguised that it renders [teachers] acquiescent to

power without their realizing it” (Greene, 1988, p. 133). Then,

students and teachers accept traditional methods used to teach

and learn mathematics as natural (Greene, 1988) without

considering the complexity of inequity (Wang et al., 2014)

embedded in mathematics pedagogies and content. Accepting

the status quo closes space for creativity and changes in

practice that may serve all students more effectively.

Dismantling inequitable customs moves teachers from

“certainty to uncertainty [which is] what I call fear… [teachers]

don’t want those patterns of existence to be disturbed”

(Krishnamurti, 1969, p. 42). Within a mathematics context, fear

of conflict from colleagues or insecurity from teaching

differently than personal experiences teaching and learning

stagnates change. Consequently, many teachers “submit” to a

system (Greene, 1988, p. 124), such as mainstream pedagogies,

whether or not they understand their allegiance. The quiet force

of hegemony hinders progress by conditioning personal beliefs

and behaviors to match systems rather than seeking alternate

paths “against the grain” (hooks, 1994, p. 26), sometimes

alone.

Institutional Barriers to Equity in Mathematics Classrooms

Reflection on dominant discursive and institutional forces

within mathematics education provides crucial ground to work

toward educational equity because mathematics possesses

gatekeeping power for college and careers (Cobb & Russell,

2015; Davis & Martin, 2008; Gutiérrez, 2012; Moses & Cobb,

2001). I start by examining the systems of thought that

seductively influence mathematics teachers’ daily practices to

move from the hegemonic pulls toward acquiescence to critical


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action. Equity situates both within individual and institutional

factors, perpetuating white supremacy. White supremacy is the

way “racial patterns adapt in ways that maintain white

dominance” (Bell, 2005e, p. 386). The structure of schools,

assessments, and instruction in mathematics perpetuate white

standards and norms for success, continuing and legitimatizing

white supremacy (Davis & Martin, 2008; Martin, 2012).

Assessment socialization and achievement orientation.

Assessments have become normative, part of the way schools

operate and analyze student achievement. An achievement

focus—including tangible results like standardized test scores

or participation—reinforces the status quo around who

qualifies to move into certain classes, colleges, career, and

economic pathways (Gutiérrez 2012). For example, No Child

Left Behind (NCLB) Act of 2001 (NCLB, 2002) intended to

increase accountability for all students, but it also augmented

assessment as the normative center of mathematical success,

creating a climate of “assessment socialization” (Cobb &

Russell, 2015, p. 632) where testing seems natural. Legislated

mandates pressure both teachers and school systems to perform

on standardized tests, scoring district, school, and teacher

efficacy on achievement and growth scores. Signed in 2015 to

replace NCLB, the Every Student Succeeds Act (ESSA)

intended to reduce the frequency of mandated testing,

providing states with more authority around accountability

measures. Whether or not this legislation alters the milieu of

assessments depends on states, districts, and individuals to

dissemble assessment mentalities.

Moreover, assessments carry immense significance for

equity because white students’ performance serves as the

reference point for achievement (Davis & Martin, 2008;

Martin, 2012), reinforcing a supposedly neutral and objective

standard centered on white students. Achievement and access

to resources, often called “opportunity to learn” (Cobb &

Russell, 2015, p. 636), reinforce white dominance (Gutiérrez,

2012), signifying people as certain types of learners because of

their race. Dominance emerged historically in science and

politics, and assessments reinforced beliefs about the

“intellectual superiority of whites” (Davis & Martin, 2008, p.

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15). Standardized assessments underestimate students of color,

in part because of the consistent exposure to deficit discourses

(Cobb & Russell, 2015). Martin (2012) contended achievement

focuses on if rather than how Black students learn, a gap-

gazing view that deficitizes students by disregarding causes—

including structural—of achievement. Thus, the wide

acceptance of rhetoric about achievement gaps, determined in

large part by assessments, unintentionally supports the “social

construction of Black children as inferior and lacking in

intelligence” (Martin, 2007, p. 16). Assessments reify norms

and ideologies around a white center, legitimizing inequity and

justifying hierarchical rankings and differential treatment

regarding career and education opportunities (Harris, 1995).

Therefore, lack of achievement falls on students, schools, or

teachers rather than the laws, policies, and systems creating the

conditions.

The dominant ideals of racial hierarchy surface when

students track into classes by their assessment and achievement

levels, as assessment performance and considerations of

achievement bias values and interests of the dominant group

(Alon & Tienda, 2007). Tracking drives access to colleges and

careers (Cobb & Russell, 2015; Davis & Martin, 2008; Martin,

2012; Moses & Cobb, 2001). In practice, schools often place

students of color in lower tracked classes, what Bell (2005b)

considered “second generation segregation” (p. 227). That is,

students of color and white students attend the same schools,

but not the same classes, often providing different content and

pedagogical practices (Boaler & Staples, 2008). Veteran

teachers rarely push to untrack classes as it requires the

challenging work of altering content and instruction

significantly (Cobb & Russell, 2015) to switch from

mathematics as skill-based to contextualized, embedded

concepts (Boaler & Staples, 2008). Tracking or de-tracking

does not create or eliminate inequity by itself; regardless,

teachers must present strong content and pedagogies across

classes (Gutiérrez, 2012).

Mainstream instruction: “Banking” educational

models. While reform mathematics emphasizes discourse and

problem solving (National Council of Teachers of Mathematics


64

[NCTM], 2000), students of color largely remain in procedural-

based mathematics classes (Boaler & Staples, 2008). These

classes often use what Freire (2011) characterized as “banking”

education, positioning students as receptacles to be filled by

teachers. Banking education seeks compliant, manageable

students: the easier students allow themselves to be filled, the

better the students they are (see also Sfard, 1998). Alone,

banking ignores community and culture, leading to the type of

teaching Martin (2007) describes as “chalkboard-focused,

technical, teacher-dominated, and … sink-or-swim” (p. 19).

With the focus on absorbing knowledge, students do not gain

critical consciousness, the ability to analyze the world and

mathematics relation to it (Aguirre et al., 2013; Gutstein, 2012;

Moses & Cobb, 2001). Using mathematics for critical

consciousness by connecting it to community or societal

realities provides avenues for equity, as I discuss later.

This section delineated the normative features of schooling

such as assessments, tracking, and compliance bolster

dominant narratives. Dominant narratives inculcate individual

beliefs; thus, individual and institution interdepend, cyclically

reinforcing each other.

Individual Mindsets Informed by Institutions

In this section, I connect institutional features and

historical consciousness to individual beliefs and pedagogies

informing practice.

Racist mindset. Many white people do not talk about race (Lensmire, 2014; Smith, Constantine, Graham, & Dize, 2008),

creating challenges in building teachers’ and students’ critical

consciousness. Instead, teachers often ascribe to the simplistic

idea that integration predominantly stopped racism in

institutions (Bell, 2005b), thinking racism only endures

individually, more of “matter of opinion” than “racism itself”

(Smith et al., 2008, p. 342). Jones (2000) described society’s

primary perception of racism to be “personally mediated” (p.

1212), revolving around prejudice, intentions, and differential

beliefs about capability. This type of racism typically occurs

between individuals, such as in interactions where someone

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says something that offends the other person. Blatant,

discriminatory actions and words do happen; however,

contemporary racism also involves the pernicious, less overt

beliefs and ideologies of individuals that emerge in institutions

and policies to drive differential impact, access, and success

(Jones, 2000).

While contemporary racism exists, many people spin

racism away from themselves (Smith et al., 2008), believing it

external from them and, therefore, downplaying the role of

race—including their own—in individual and societal events.

For example, teachers use personally mediated racism when

they provide varied instruction across classes, with lower level

classes often occupied predominately by students of color and

often receiving mainstream instruction (Boaler & Staples,

2008). When teachers explain differential instruction with a

deficiency in the students’ culture or capability rather than

considering societal structures, curriculum, instruction, or their

beliefs, the teacher spins racism away from themselves and

institutions, rendering student-centered change difficult.

As a solution, some teachers attempt to bridge students’

lives with mathematics by using culturally relevant teaching

practices (Gay, 2000; Ladson-Billings, 2009). However,

without deconstructing the racialized mentalities about students

and communities that inform mathematics classroom, they

often still marginalize students of color (Martin, 2012).

Dominant ideology’s influence on individual practice and

beliefs then eludes teachers, and blame shifts from systemic

racism to individual teachers or students. Teachers often do not

contextualize Black children within the students’ social

realities but, rather, through dominant (white) frames of

reference (Martin 2012). Teaching mathematics through a

dominant ideology— “their own personal views of reality”

(Freire, 2011, p. 94)—rather than considering experiences of

students of color uses a colorblind ideology (Bonilla-Silva,

2002). Martin (2007) equated colorblindness with cannibalism:

“teaching students without really ‘seeing’ them” (p. 19).

Teacher’s (often subconscious) beliefs about race and about

particular groups inform instructional decisions, including how

they position students mathematically. The “subtle, apparently


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non-racial” (Bonilla-Silva, 2002, p. 42) practices of avoiding

racial discussion, spinning away the role of race, and not

viewing students within the full context of their lives create an

institutional level system of contemporary, colorblind racism

and maintain white supremacy.

Jones (2000) described the institutionalized level of racism

as practices that provide different access to resources or

opportunity by race, either through law or normalization. In

mathematics classrooms, the differential access to high-quality

coursework across race reflects institutionalized racism,

“codified in our institutions of custom, practice, and law, so

there need not be an identifiable perpetrator” (p. 1212);

individual practices become the institution. Tracking students

into classes based on discrete measures and providing

remediation-oriented rote instruction becomes normal and

mechanizes inequities’ persistence (Boaler & Stapes, 2007).

Math content and pedagogy become static knowledge, passed

via banking models, rather than transactional and critical

(Frankenstein, 1983; Freire, 2011). Thus, mindsets diminish the

role of race and block asset-oriented, equitable teaching and

effective learning for students of color (Aguirre et al., 2013).

“Missionary” or “cannibal” mindset. Because of deficit

thinking, achievement orientation, and colorblind racism,

Martin (2007) maintained teachers often interact with their

students of color either as “missionaries” or “cannibals” (p.

23). Sometimes teachers of color, too, enact missionary or

cannibal stances because of internalized (Jones, 2000) racist

norms and stereotypes about their racial group influence how

they see themselves and their students. For example, if a

teacher of color uncritically accepts standardized assessments

(both the practice and the results) without deconstructing the

connected inequities, they may have internalized the neutrality

of tests and adopted the tests’ racial categorization that places

students of color at the bottom. As missionaries, teachers feel

that they must save and “insulate poor black children from the

risks of ghetto life” (Bell, 2005c, p. 269)—a form of cultural

racism that deems home cultures of certain races as detrimental

to their success (Bonilla-Silva, 2003). Cultural racism surfaces

in some educational programs such as Knowledge Is Power

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Program (KIPP) schools where long school days and the

requirement for students to call teachers with all homework

questions (Mathews, 2009) perhaps serves to protect students

from their home lives.

Even when well-intentioned, teachers cannot escape savior

ideologies if they do not engage their students with

academically rigorous and relevant teaching practices fitting

their sociocultural identities (Martin, 2007). Freire (2011)

disavowed treating students as objects to be saved, especially

without embracing student agency and engaging personal

reflexivity. Conversely, without commitment to students and

their sociocultural lives, teachers act as cannibals, destroying

students’ assets within the classroom and instead assimilating

normative thinking and behaviors. Brown v. the Board of

Education’s (1954) desegregation of schools demonstrates the

mentalities of missionary or cannibal toward Black students.

People considered white schools an improvement regardless of

the circumstances (missionaries) and/or primarily ignored

students of color as they integrated into the school system,

minimizing students of color and their experiences in school

spaces (cannibals; Bell, 1980, 2005b).

Meritocratic mindset. Colorblindness also emerges in the

U.S.’s script for success: Individuals hold the freedom and

power to advance, educationally or otherwise (Greene, 1988;

Wang et al., 2014; West, 1989). American culture focuses on

creative democracy, individuals’ ability to use their intellect

and resources to transform the world (West, 1989).

Individualism and meritocracy, a belief that the merit and hard

work of individuals creates success, highlights individual

qualities, rather than institutional barriers (Bell, 2005c;

Chakravartty & da Silva, 2012; Wang et al., 2014). For

example, schools analyze standardized test performance by the

efforts and performances of individuals, not the structures of

society, education, or the discourse surrounding the test-taker.

The ideology of the American Dream preserves the

ahistorical, individualistic belief that each person holds the

responsibility and freedom for their decisions (Bell, 2005d;

Greene, 1988) rather than taking into account the influence of

laws, policies, and actions intended to disenfranchise. Not


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remnants of the past, inequitable laws serve the on-going

kinesis of racism that maintains relationships of power over

time (McAfee, 2014; Thompson Dorsey & Venzant Chambers,

2014). For example, police stop and arrest more people of color

(White, 2015), standardized tests preference white students

(Aguirre et al., 2013; Cobb & Russell, 2015), and home loan

policies maintain racial debt (Chakravartty & da Silva, 2012).

The belief in institutional and legal equality ignores the on-

going racial dynamics knit into our history, ideologies, and

institutions.

However, many white teachers adopt colorblind mentalities

and pedagogies to avoid the discomfort and fear that

accompanies deep grappling with the material realities of

racism, instead maintaining their relative comfort and

superiority in the face of changing societal demographics and

mentalities (Harris, 1995). Teachers want to believe that

inequities in achievement stem from cultural or natural factors

or students’ lack of hard work rather than discrimination.

Otherwise, they may uphold white supremacy and their success

may come from unearned privileges (Bonilla-Silva, 2002;

Bonilla-Silva, 2003; Ghabra, 2015). Meritocratic rhetoric

emerges around programs like affirmative action, programs

that broaden admission criteria to be more inclusive of various

student qualities to increase access to college for students from

historically marginalized backgrounds. If meritocracy worked,

then affirmative action would be “reverse discrimination”

(Bonilla-Silva, 2002, p. 51), but if individual and institutional

factors hinder the success of some groups, then affirmative

action attempts to address systemic issues (Harris, 1995).

Consequently, meritocracy blocks efforts to address the deep

structural fissures maintaining inequity (Cobb & Russell,

2015). Meritocratic stances perpetuate the comfortable but

oppressive dominant perspectives toward students of color in

mathematics, stymying alterity and upholding white

supremacy.

Deficit mindset. Teachers’ deeply rooted prejudices and

stereotypes, born from institutions and societal power

dynamics, underlie the achievement of students of color.

Deficit views stem from history, science, media, and

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authoritative discourse. These views position students of color

and their communities, families, and values as pathological.

Without deconstruction, deficit mindsets often consciously or

unintentionally impact teachers’ perceptions and practices so

they do not supply rich learning opportunities and

environments (Martin, 2012). Bonilla-Silva (2003) defined this

as cultural racism wherein (mostly) white people attribute

differential outcomes to a lack within a culture. White teachers

may lack the experiences and understanding to overcome stock

images and deficit mindsets. For example, I interiorized beliefs

of Native Americans as savage and my superiority until I

worked with a summer program for Native American students

that disrupted and forever altered my stock beliefs. Likewise,

teachers may shift blame toward students and families without

making sense of their students’ realities (Martin, 2007) and

capabilities (Yosso, 2005) or having the requisite experiences

to dismantle harmful beliefs.

Deficit mindsets relate to colorblind racism and imply that

“good teaching is transcendent” (Martin, 2007, p. 18).

Teachers, thus, view students of color as white children who

need more help attaining white achievement (Martin, 2007).

Recognizing their inefficacy with students of color, teachers

neglect the complexity of factors influencing how students of

color learn, position students as lacking (Aguirre et al., 2013),

and limit their perception of student ability (Martin, 2007) to

preserve a positive self-image. Newton (2002) distinguished

between Western society that largely views contradictions such

as racist and not racist as external, so a person can be either

racist or not. In societies that view contradiction as internal,

such as in African societies, all people hold both racism and

resistance to racism. The degree to which behavior and

thoughts evince one aspect of the contradiction over the other

depends upon the level of critical examination and subsequent

actions, an ever-shifting dynamic. When people consider the

complexity in holding internal contractions with both “good”

and “bad” pieces, they can face the racist aspects of themselves

without the immobilizing fear of being wholly racist.

Often avoided because of colorblindness, teachers’

perceptions of capability tied to race influence student success


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and mathematical identity. Even when Black students come

from the middle-class or higher, they typically “encounter

ideologies of Black intellectual inferiority” (Martin, 2012, p.

52), stereotypes and biases that situate them as less capable

academically. Deficit ideologies negatively influence students

view of themselves as mathematics learners and their

subsequent achievement (Aguirre et al., 2013). Race, not the

socioeconomic reasons commonly cited within cultural racism

that minimizes the role of race, predicts mathematics

achievement over economic class (Martin, 2012; Singleton &

Linton, 2006). Rather than dialoguing about the pervasiveness

of race on economic and educational outcomes, Singleton and

Linton (2006) described the school systems’ focus on

socioeconomic factors as circumlocution of the deep impact of

race and culture on students. Similarly, individuals and

educational systems must name and deconstruct the centrality

of race to move toward equity (Crenshaw et al., 2006).

In this section, I named the strands influencing

mathematics classrooms where Black and Latinx students

occupy the lowest achievement levels. I juxtaposed the

individual mindsets of colorblindness, meritocracy, and

individualism with the institutional features of schools that

include assessment socialization and the primacy of

achievement, always to a white norm. Together, normative

dimensions construct an on-going educational milieu that

serves white students most effectively while reifying inequity.

Avenues to Critical Consciousness: The Convergence of

Interest and Identity

In this section, I ponder entry points toward institutional

change using Bell’s (2005a) concept of interest convergence,

the idea that racial equality will come when it benefits white

economic and sociopolitical interests. Then, I consider the

institutional influence on individuals to argue for the moral and

humanizing necessity for change. The individual moral

imperative must connect with institutional factors and extend

beyond the frameworks of naming privilege and racial identity.

Transformation requires reflection and action toward identity

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convergence (see also Greene, 1988), the understanding that

alteration requires interconnectedness of various backgrounds

and races and the mutual pursuit of a “project” (p. 17)—in this

case, mathematical equity.

Interest Convergence

Economic factors. Economic incentives exist to reward

schools for student achievement on assessments, and many

schools plaster posters with statistics of lifetime earnings by

education level to motivate students to achieve. But, economic

competition breeds fear of other people’s success diminishing

their own (West, 1989), causing people to latch onto their

status and view resources through competition rather than

seeing their struggle as part of the human collective (Harris,

1995).

Bell (2005a) depicts the historic economic reality of

slavery, where a few plantation owners maintained the bulk of

the wealth. Rather than the economically-dispossessed working

class whites and slave uniting to resist exploitation, ruling

whites convinced working class whites that whiteness gave

power, inscribing racial superiority with economic status and

bolstering racial hierarchy (Harris, 1995). Lensmire (2014)

argued white people consume stereotypes about people of color

as a “scapegoating rite” (p. 6) to ensure racial superiority and

economic position. Consequently, political and legal changes

occur most readily when they serve the white power

structure—and, therefore, are not enough to create paradigms outside of the white center. For example, Bell (2005b) argued

the Civil Rights Movement and Brown v. Board of Education

transpired because economic benefits converged in the interest

of the white power structure. Civil Rights’ success occurred

because it maintained the comfort and position of most white

people (Greene, 1988), even benefitting them. Damaged by

segregation in the perceptions of the world, Bell (1980)

asserted that the U.S. needed to solidify the appeal of

democracy against communism, prevent the dissatisfaction and

subsequent violence of Black veterans of World War II, and

facilitate Southern industrialization. Therefore, interest


72

convergence necessitated policy changes to civil rights and

educational systems while maintaining white supremacy

through increased backing for U.S. democracy, building the

U.S. economy in global and local matters, and neutralizing

resistance by people of color.

U.S. society maintains relative affluence globally, but

inadequate systems of health care, education, and childcare

comparatively reflect its continued white supremacist power

structure (Bell, 2005d). Failure to address basic social

necessities roots in racist and deficit beliefs; many white people

interiorize stereotypes that equate supporting social programs

with bailing out people of color—subsidizing lazy people or

criminals (Bonilla-Silva, 2003). These constructions stem from

the individualism of the white economic elite, who strives to

sustain their standing (Harris, 1995).

Just as slave-owners garnered support from working class

whites against slaves by focusing on the social benefit of white

superiority, conflating “issues of race and economic neglect

serves to rationalize the policies of inaction” (Bell, 2005d, p.

329). For example, deficit perspectives that consider people of

color as less deserving of education since they are lazy or

criminal (da Silva, 2001) justify inadequate funding of urban

public schools. Dehumanizing groups of people through

discursive packing of economic deservedness destructs notions

of democracy, freedom, and equality. Educators must unpack

colorblind racism and meritocracy because they allow people

to rationalize disadvantages by socioeconomic class, cultural

deficiencies, or a lack of work ethic rather than addressing the

salience of race (Singleton & Linton, 2006). To Bell (2005d),

“deepset racial fears [are] the real barrier” (p. 330) to economic

and mathematical equity.

The economic benefits of supporting the mathematical

success of all students—not only the white, male norm—will

take years to realize, after initial economic costs of investing in

teachers, teacher training, and rethinking curricula, school

structures, and relationships between teachers and students.

However, Moses and Cobb (2001) insisted on mathematics

pivotal role in racial progress. The initial cost burdens of

pursuing mathematical equity overshadow the eventual

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opening of enterprise and opportunity by engaging the

collective brilliance and potential of all people. Mere inclusion

of people, however, will not achieve the necessary dismantling

of the ideologies and systems rooting white supremacy (da

Silva, 2001), deeply challenging work. Nonetheless, Leopold

(1966) posited issues must be considered beyond their

economics, but also “what is ethically… right” (p. 262) and

what will develop more human interactions between people.

Immediate changes that persist and alter systems must involve

individual development and action—not only economic

imperatives of wage, job security, or funding.

Identity Convergence Beyond Linearity

Because racial experiences inform educational decisions

and cut across lives, white teachers must avoid colorblind racist

discourse to grapple with their social identity, their engagement

with students, and math content (Aguirre et al., 2013; Bonilla-

Silva, 2002; Lensmire, 2014). Simply naming white identity

development and white privilege, trademarks of white teacher

development, fails to address racism with action (Smith et al.,

2008). Privilege serves a purpose of identifying and describing

inequity, but, alone, it closes the space for action, as the action

becomes only confession of privilege (Lensmire et al., 2013).

Addressing threatened concepts of white humanity and self-

image serve important loci of reflexivity, but they also may

create defensiveness and less openness without additional

unpacking or action. Since white privilege is an effect of white supremacy, not the cause, naming alone both does not address

structural roots of privilege and creates paralysis for white

people. Instead, individual privileges must be identified and,

moreover, connected to the institutions that maintain the

privilege. Then, teachers can interrogate their privilege in the

context of systems to conceive of systemic alternation,

realizing the interconnection between privilege and history.

White people must address the historical roots of racism

without discursive avoidance of complicity by deploying a

fixed and teleological view of racism as relic.


74

Interrogating teacher identity and privilege should consider

historical complexity and nonlinearity while also focusing on

student learning (Lensmire et al. 2013; Martin, 2012).

Lowenstein (2009) recognized the discursive process of equity

work, requiring the experiences of white teachers as an opening

for discussion. The “philosophical and ideological

underpinnings” (Ladson-Billings, 2009, p. 162) of teachers’

view of themselves and their students undergirds how they

structure classroom interactions, conceptualize knowledge, and

frame knowledge construction. Therefore, teaching

environments rely on teacher perception of students, but also

on the teacher’s sense of self. Teachers must possess a strong

self-concept (Wang et al., 2014; West, 1989) and view

themselves as effective while also interrogating their practice

to increase their success and vision (Aguirre et al., 2013).

Greene’s (1988) continuum provides a nuanced process for

white teachers to build mathematical equity, cycling

nonlinearly between critical consciousness, reflective

resistance, and action.

Mechanisms of Asset-Oriented Teacher Growth

Critical consciousness: Seeing and naming the world.

Greene (1988) defined consciousness as “seeing what [is]

normally obscured by the familiar” (p. 122) to interrogate the

world. Critical questions allow people to see beyond

“fragments” (Freire, 2011, p. 104) and stereotypes to

participate in dialogue, discover nuance, and uncover possibilities for transformation. Strong, critical leadership and

support of colleagues moves teachers from using avoiding

conflict with colorblind ideologies to addressing inequity

directly and working through conflict (Lensmire, 2014; Matias,

2016). Educators must center race to push mathematics

communities and re-imagine mathematics education,

dialoguing about how hegemonic individual and institutional

factors surface in their classroom and schools.

Reflective resistance: Strong self-concept and

contemplation. Naming and dialogue alone do not prompt

transformation; the “problematics of power, agency, and

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history” (Freire, 2011, p. 17) must be connected to identity and

experience (Greene, 1988). Reflexivity examines the interplay

between the personal and the institutional. Analyzing the

various interlinks between self, mathematics content,

pedagogy, and systems demands both time and commitment

(Aguirre et al., 2013). It requires dismantling normative

conditioning and addressing individual complicity upholding

white supremacy. It requires facing the role history in shaping

the present, particularly the role of racism. It requires openness,

authenticity, humility, and communication with students and

communities to unlearn and relearn. When teachers do engage

a critical perspective “in search of [their] own freedom”

(Greene, 1988, p. 14), they open space for students. Then,

teachers, students, and parents share responsibility for

mathematical learning and embrace their strengths to begin the

process of transformation (Aguirre et al., 2013).

Action. People often wait for a leader to compel action

(Bell, 2005d), rather than recognizing how their minute actions

affect institutions. Critical action toward transformation stems

from reflection (Freire, 2011) and self-belief (Wang et al.,

2014). Greene (1988) argued self-concept cannot remain “as an

interiority” (p. 21); once educators recognize the world’s

mechanization of racism and their complicity within it, they

must act. Reflexivity establishes angst as individuals realize the

dimensionality of injustice, and this augments to action.

Assessment-based accountability will not press change because

tests bias by race; teaching to white norms, then, can produce

test results that bolster achievement within current

accountability systems. Thus, a “humanizing pedagogy”

(Freire, 2011, p. 68) insists that teachers extend beyond the

teaching structures and strategies of their experiences and

traditions (Moses & Cobb, 2001) to the human need of

dismantling racism.

Avenues to Enter: Action

What will converge teacher identity to equitable instruction

beyond the models and institutions they know? I provide

spaces to enter the complex work of altering practice for equity


76

as teachers’ identities toward mathematics, themselves, and

their students either reifies or disrupts inequity. Aguirre et al.

(2013) recommended teachers start with naming and reflection,

perhaps by writing a mathematical biography because the most

impactful alterations of practice will follow intentional

reflection. Teachers, then, can create a practice-reflection

cycle, constantly building their “vision for mathematics” (p.

119) to share with parents through letters and conferences (see

Aguirre et al., 2013 for examples). Parents can help co-

construct the mathematics community through feedback and

participation in class, thus incorporating expanded ideas of

capital—called cultural wealth—in the classroom such as the

strengths of familial connection (Yosso, 2005).

Teachers can use models (Aguirre et al., 2013; Boaler &

Staples, 2008; Frankenstein, 1983; Gutstein, 2012; Leonard,

2008; Moses & Cobb, 2001) of “problem-posing” (Freire,

2011, p. 81) education to build students’ critical consciousness

of the world. For example, in Aguirre et al. (2013), a teacher

and his students collected and mathematically analyzed school

data regarding the claim that the school suspended a student for

“being Mexican” (p. 50). With confidence and purpose, the

students used mathematics to relate to their social positions and

serve as a tool for understanding the world. Additionally,

Moses and Cobb (2001) recommended nonlinear teaching

practices to help students build conceptual knowledge such as

discussing the problem in their own language and using

symbols to represent their ideas. Students work from what is

concrete and understandable to them—their body, their

drawings, their language—as an entry to understanding

complex mathematics. Concretizing mathematics for students

avoids the frustration and negative identities that surface in the

abstract (Moses & Cobb, 2001).

Teachers must also reflect on what and how they assess,

interrogating the content and use of assessment to create

alternatives that broaden conceptions of competence, such as

mathematics journals (see Aguirre et al., 2013 for specific

guidelines). Mathematics journals can provide students space

to think and make important mistakes, promote high-level

discourse and multiple solution methods, reinforce

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77

mathematical identities, and shift responsibility for learning to

students (Hufferd-Ackles, Fuson, & Sherin, 2004). Teachers

can use targeted, narrative feedback to shift from grade-

oriented to growth-oriented (Aguirre et al., 2013). Boaler and

Staples (2008) recommended de-tracking classes to provide

high-quality, conceptual instruction for all students that

incorporates varied forms of capital for collective learning.

Regardless of whether schools de-track, teachers and schools

must consider how assessments place students into

mathematics classes and what mathematics experiences they

provide across classes.

Implications and Next Steps

Transformation will occur if individuals perceive and

reflect to the point of action where they cannot continue life in

stasis (Greene, 1988). “An amalgam of… necessity, chance,

and, most importantly, love” (West, 1989, p. 52) drives

evolution, and teachers and teacher educators must not rely on

economic necessity or job mandates. Instead, they must move

beyond fear to realize that their fullness of self—and resistance

to complicity in injustice—requires interrogating the living

realities of racial inequity that root historically, engaging with

the sometimes-painful work of praxis. Interior work toward

person freedom encourages others, including other educators

and students, to do the same. Together, the individual strands

of deep grappling compose a web of critical consciousness that

can nuance and alter what is currently known. But, questions and spaces for further work remain: How can we frame racial

dialogue and gain tools to work through honesty and conflict

without becoming immobilized or hopeless? How can we

embrace plurality of students and selves, connecting for

transformational mathematics, especially given competing

demands on time and energy? How can we gain the

competence and imagination to work differently than our daily

experiences and what we have been told? What languages,

frameworks, and strategies would allow us to consider the

complex and kinetic nature of racial contradiction, operating

both institutionally and within us? Because of its complexity,


78

equity—pushed by identity convergence—requires

commitment and growth, necessitating that we move beyond

“simplistic remedies that cannot work” (Eisner, 1998, p. 115).

As Greene (1988) described, “At the point of encounter there

are neither utter ignoramuses nor perfect sages; there are only

people who are attempting, together, to learn more than they

now know” (p. 90). Therefore, we must guide each other and

our institutions by focusing on ourselves. Progress emerges

from the intersection of individual and institutional, starting

with each individual.

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